Chapter 19, Problem 25E

(a)

To determine

To explain do you expect the $95\%$ confidence interval for the true proportion of all $18-\text{to}29-$ year-olds who are worried to be wider or narrower than the $95\%$ confidence interval for the true proportion of all U.S. consumers.

Answer to Problem 25E

It is wider.

Explanation of Solution

It is given in the question that Experian/Gallup personal credit index poll of $1008$ U.S. adults aged $18$ and over $8\%$ of respondents said they were very uncomfortable with their ability to make their monthly payments on their current debt during the next three months. A more detailed poll surveyed $1288$ adults reporting similar overall results and also nothing differences among four age groups. Thus, we expect the $95\%$ confidence interval for the true proportion of all $18-\text{to}29-$ year-olds who are worried to be wider than the $95\%$ confidence interval for the true proportion of all U.S. consumers because the sample size is probably about one-fourth of the sample size for all adults as we had expect the confidence interval to be about twice as wide.

(b)

To determine

To explain do you expect this second poll’s overall margin of error to be larger or smaller than the Experian/Gallup’s poll.

Answer to Problem 25E

It is smaller.

Explanation of Solution

It is given in the question that Experian/Gallup personal credit index poll of $1008$ U.S. adults aged $18$ and over $8\%$ of respondents said they were very uncomfortable with their ability to make their monthly payments on their current debt during the next three months. A more detailed poll surveyed $1288$ adults reporting similar overall results and also nothing differences among four age groups. Thus, we expect this second poll’s overall margin of error to be smaller than the Experian/Gallup’s poll because the second poll used a slightly larger sample size than the first one.